\subsection*{实验3.最小偏向角法测量棱镜的折射率}
\subsubsection*{(1)原始数据记录表格}

\begin{tabular}{|c|c|c|c|c|c|c|}
\hline 
\multicolumn{2}{|c|}{次数} & 1 & 2 & 3 & 4 & 5 \\ 
\hline 
\multirow{2}{*}{\text{入射角}}
& ${\alpha}_1$ 
{% for a in ANGLE_A1_MIN %}
& %% a.angle %%$^{\circ}$%% a.minus %%'
{%- endfor %}
\\  
\cline{2-7}
& ${\beta}_1$ 
{% for a in ANGLE_B1_MIN %}
& %% a.angle %%$^{\circ}$%% a.minus %%'
{%- endfor %}
\\ 
\hline 
\multirow{2}{*}{\text{折射角}}
& ${\alpha}_2$ 
{% for a in ANGLE_A2_MIN %}
& %% a.angle %%$^{\circ}$%% a.minus %%'
{%- endfor %} 
\\ 
\cline{2-7}
& ${\beta}_2$ 
{% for a in ANGLE_B2_MIN %}
& %% a.angle %%$^{\circ}$%% a.minus %%'
{%- endfor %} 
\\ 
\hline 
\multicolumn{2}{|c|}{${\delta}_{min}$} 
{% for a in ANGLE_DELTA_MIN %}
& %% a.angle %%$^{\circ}$%% a.minus %%'
{%- endfor %}\\ 
\hline 
\end{tabular} 
\vspace{10pt}

\begin{center}
${\delta}_{min}$是最小偏向角，且有${\delta}_{min}=\displatstyle\frac{1}{2}[({\alpha}_2-{\alpha}_1)+({\beta}_1-{\beta}_2)]$
\end{center}

${\delta}_{min}$的平均值为：$$\bar{{\delta}_{min}}=\frac{1}{5}\sum\limits_{i=1}^{5}{{\delta}_{min}}}=%% AVERAGE_MIN %%rad$$

$$n_1=\displaystyle\frac{\sin{\frac{{\delta}_{min}+A}{2}}}{\sin{\frac{A}{2}}} = \displaystyle\frac{\sin{\frac{%% AVERAGE_A %% + %% AVERAGE_MIN %%}{2}}}{\sin{\frac{%% AVERAGE_A %%}{2}}} = %% N1 %%$$

${\delta}_{min}$的A类不确定度：
$$u_a({\delta}_{min}) = \sqrt{\displaystyle\frac{\sum\limits_{i=1}^{5}({\delta}_{min}-\bar{{\delta}_{min}})}{5{\times}(5-1)}^2 } = %% UA_MIN %%rad$$

${\delta}_{min}$的B类不确定度：
$$u_b({\delta}_{min})=\displaystyle\frac{\bigtriangleup\text{仪}}{\sqrt{3}}
= \frac{1'}{\sqrt{3}} = \frac{\pi}{180\times60\times\sqrt{3}} = 1.6794 \times 10^{-4}rad$$

${\delta}_{min}$的不确定度：
$$u({\delta}_{min}) = \sqrt{u^2_a({\delta}_{min})+u^2_b({\delta}_{min})} = %% U_MIN %%$$

$$u(A) = %% U_A %% $$

$$u(n_1) = \sqrt{(\frac{{\partial}n_1}{{\partial}{\delta}_{min}})^2{\times}u^2({\delta}_{min})+(\frac{{\partial}n_1}{{\partial}A})^2u^2(A)} = %% U_N1 %% $$
